Going further in this direction, in the case when \(f\)  is a cusp form of half-integral weight with real Fourier coefficients contained in the plus space, Kohnen and Bruinier [1]} gave the conjecture
\(\lim _{x\rightarrow \infty }\dfrac{\#\lbrace n\le x\; :\; a(n)\gtrless 0\rbrace }{\#\lbrace n\le x \; :\; a(n)\ne 0\rbrace }=\frac{1}{2}.\) 
